Minimal unitary representation of SU(2,2) and its deformations as massless conformal fields and their supersymmetric extensions

Journal Article · Sun Aug 15 00:00:00 EDT 2010 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.3447773· OSTI ID:21476529

Fernando, Sudarshan; Guenaydin, Murat ^[1]

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1. Department of Physical Sciences, Kutztown University, Kutztown, Pennsylvania 19530 (United States)

We study the minimal unitary representation (minrep) of SO(4,2) over a Hilbert space of functions of three variables, obtained by quantizing its quasiconformal action on a five dimensional space. The minrep of SO(4,2), which coincides with the minrep of SU(2,2) similarly constructed, corresponds to a massless conformal scalar in four space-time dimensions. There exists a one-parameter family of deformations of the minrep of SU(2,2). For positive (negative) integer values of the deformation parameter {zeta}, one obtains positive energy unitary irreducible representations corresponding to massless conformal fields transforming in (0,{zeta}/2)((-{zeta}/2,0)) representation of the SL(2,C) subgroup. We construct the supersymmetric extensions of the minrep of SU(2,2) and its deformations to those of SU(2,2|N). The minimal unitary supermultiplet of SU(2,2|4), in the undeformed case, simply corresponds to the massless N=4 Yang-Mills supermultiplet in four dimensions. For each given nonzero integer value of {zeta}, one obtains a unique supermultiplet of massless conformal fields of higher spin. For SU(2,2|4), these supermultiplets are simply the doubleton supermultiplets studied in the work of Gunaydin et al. [Nucl. Phys. B 534, 96 (1998); e-print arXiv:hep-th/9806042].

• OSTI ID: 21476529
• Journal Information: Journal of Mathematical Physics, Vol. 51, Issue 8; Other Information: DOI: 10.1063/1.3447773; (c) 2010 American Institute of Physics; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
CONFORMAL INVARIANCE
HILBERT SPACE
IRREDUCIBLE REPRESENTATIONS
MASSLESS PARTICLES
QUANTUM FIELD THEORY
SCALARS
SO-4 GROUPS
SPACE-TIME
SPIN
SU-2 GROUPS
SUPERMULTIPLETS
SUPERSYMMETRY
UNITARY SYMMETRY
YANG-MILLS THEORY
ANGULAR MOMENTUM
BANACH SPACE
ELEMENTARY PARTICLES
FIELD THEORIES
INVARIANCE PRINCIPLES
LIE GROUPS
MATHEMATICAL SPACE
MULTIPLETS
PARTICLE PROPERTIES
SO GROUPS
SPACE
SU GROUPS
SYMMETRY
SYMMETRY GROUPS